The amendment changes the rules of Parliament for a day (March 27) to allow government business to be superseded by a motion relating to Brexit. This will allow the House of Commons to hold a debate, and, subsequently, vote, on alternative Brexit outcomes without the Government intervention.

Amendment (a) moved, at end, add “and, given the need for the House to
debate and vote on alternative ways forward, with a view to the
Government putting forward a plan for the House to debate and vote on,
orders that –

(a) Standing Order No. 14(1) (which provides that government business
shall have precedence at every sitting save as provided in that order)
shall not apply on Wednesday 27 March;

(b) precedence on that day shall be given to a motion relating to the
Business of the House in connection with matters relating to the
United Kingdom’s withdrawal from the European Union other than any
Business of the House motion relating to the consideration by the
House of a motion under Section 13(1)(b) of the European Union
(Withdrawal) Act 2018, and then to motions relating to that withdrawal
and the United Kingdom’s future relationship with the European Union
other than any motion moved under Section 13(1)(b) of the European
Union (Withdrawal) Act 2018;

(c) if more than one motion related to the Business of the House is
tabled, the Speaker shall decide which motion shall have precedence;

(d) the Speaker shall interrupt proceedings on any business before the
Business of the House motion having precedence at 2.00 pm on Wednesday
27 March and call a Member to move that motion;

(e) debate on that motion may continue until 3.00 pm on Wednesday 27
March at which time the Speaker shall put the questions necessary to
dispose of proceedings on the motion including the questions on
amendments selected by the Speaker which may then be moved;

(f) when those proceedings have been concluded, the Speaker shall call
a Member to move one of the other motions having precedence;

(g) any proceedings interrupted or superseded by this order or an
order arising from the Business of the House motion may be resumed or
(as the case may be) entered upon and proceeded with after the moment
of interruption on Wednesday 27 March.".—(Sir Oliver Letwin.)

The amendment supplements the text of the motion proposed by the government:

That this House, in accordance with the provisions of section 13(6)(a) of the European Union (Withdrawal) Act 2018, has considered the Written Statement titled "Statement under Section 13(4) of the European Union (Withdrawal) Act 2018" and made on Friday 15 March 2019.

Correction: it's not an amendment to the Withdrawal Act. The Government proposed a motion that said, basically "Yes, the House of Commons has received a statement from the Government, as required under Section 13 of the Withdrawal Act". The Letwin Amendment tacks on "...and here's what the House is going to do about it".
– owjburnhamMar 26 '19 at 9:19